Question

A newly issued 10-year maturity, 6% coupon bond making annual coupon payments is sold to the public at a price of $920. What will be an investor’s taxable income from the bond over the coming year? The bond will not be sold at the end of the year. The bond is treated as an original issue discount bond. (Round your answer to 2 decimal places.)

Taxable Income:

Answer 1

Price of the Bond = $920 | Time to maturity = 10 years | Coupon rate = 6% | Face Value = $1000

Annual Coupon Payment = Coupon rate * Face Value = 6% * 1000 = $60

Price of a bond = Present Value of all coupon payments + Present Value of Face Value received at maturity

PV of all coupon payments = (Coupon / YTM)*(1 - (1+YTM)^-T)

PV of Face value = Face Value / (1+YTM)^T

Here, we know the Price of the bond, Coupon payment and Time. YTM of the coupon is unknown.

Putting known values in the Price of a bond formula and keeping YTM as YTM.

920 = (60 / YTM)*(1 - (1+YTM)^-10) + 1000 / (1+YTM)¹⁰

Calculation of YTM can be done using three-methods, One is Trial and Error where we try a rate and check if Left hand side of above expression equals Right Hand side, Second is a Financial Calculator where IRR can be calculated for the payments and Third is the =RATE function in excel.

For this question, I have used Excel's =RATE function.

Input for RATE function: =RATE(NPER=10,PMT=60,PV=(-920),FV=1000)

Below is the screenshot of how Function looks like in Excel and its result:

Hence, YTM of the bond is 7.14676%.

Now using the Constant Yield to Maturity assumption, we can calculate the Price of Bond after 1 year.

After 1 year, 9 coupon payments are remaining. We will use same Price of the bond formula as provided above.

Price of a bond = Present Value of all coupon payments + Present Value of Face Value received at maturity

Price of a bond = (Coupon / YTM)*(1 - (1+YTM)^-T) + Face Value / (1+YTM)^T

Coupon = 60 | YTM = 7.14676% | T = 9 years | Face Value = 1000

Price of the Bond after 1 year = (60 / 7.14676%) * (1 - (1+7.14676%)^-9) + 1000 / (1+YTM)⁹

Price of the Bond after 1 year = 839.5414 * 0.462735 + 537.2651

Price of the Bond after 1 year = 388.49 + 537.26

Price of the Bond after 1 year = $ 925.75

As Bond Price has increased from 920 to 925.75 after 1 year, the increase will be added to Taxable income of the investor.

Taxable Income = Change in Price in 1 year + Coupon Payment for first year

Taxable Income = (925.75 - 920) + 60

Taxable Income = 5.75 + 60

Taxable Income for an investor after one year = $ 65.75

Hence, Taxable income for an investor over the coming year is $65.75